Cristiano Ronaldo opened the scoring for Madrid as he chipped home Mesut Ozil's through ball after just 9 minutes.
The tie was virtually killed off 17 minutes from time after substitute Gonzalo Higuain headed home Xabi Alonso's free-kick.
It was a night of contrasting fortunes for Ronaldo and Didier Drogba, with the Ivory Coast striker unable to influence the game.
Borussia Dortmund were left to rue a host of missed chances as the quarter-final first leg against Malaga at La Rosaleda ended in a 0-0 draw.
Dortmund remain the only unbeaten team in the Champions League this season, while Malaga extended their unbeaten home record in Europe to 14 games.